Flexural tensegrity is a structural principle for which the integrity under flexure of a beam formed by a chain of segments in unilateral contact is provided by an unbonded prestressing tendon anchored to the end segments, with the possible interposition of linear springs and linear dashpots. These are activated by the inflexion of the beam as a consequence of the particular shape of the contact surfaces of adjacent segments, so to induce a nonlinear dependence of the bending stiffness and structural damping on the amplitude of the inflexion. Under simplifying hypotheses, these nonlinear effects are analyzed for the nonlinear vibrations under harmonic excitation, also considering the effects of an initial camber. A variation of the tensile force in the tendon, via an actuator, can likewise modify the bending stiffness of the beam. A harmonic variation can provoke phenomena of parametric resonance, whereas an active control permits to annihilate pre-existing vibrations. The possibility of taking advantage of the nonlinear character of the damping through the optimization of the dissipated energy is also explored.
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